\left\{ \begin{array} { l } { x - 2 y + z = 9 } \\ { 3 x + 2 y - 2 z = 4 } \\ { 2 x - 4 y - z = 9 } \end{array} \right.
Solve for x, y, z
x=4
y=-1
z=3
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x=2y-z+9
Solve x-2y+z=9 for x.
3\left(2y-z+9\right)+2y-2z=4 2\left(2y-z+9\right)-4y-z=9
Substitute 2y-z+9 for x in the second and third equation.
y=-\frac{23}{8}+\frac{5}{8}z z=3
Solve these equations for y and z respectively.
y=-\frac{23}{8}+\frac{5}{8}\times 3
Substitute 3 for z in the equation y=-\frac{23}{8}+\frac{5}{8}z.
y=-1
Calculate y from y=-\frac{23}{8}+\frac{5}{8}\times 3.
x=2\left(-1\right)-3+9
Substitute -1 for y and 3 for z in the equation x=2y-z+9.
x=4
Calculate x from x=2\left(-1\right)-3+9.
x=4 y=-1 z=3
The system is now solved.
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